This chapter provides an introduction to Bayesian statistics directed at research in the social sciences, with an emphasis on how this approach differs from traditional statistical procedures. It presents the mechanics of Bayesian inference along with the underlying theoretical justification. The chapter highlights important philosophical and practical differences between Bayesian methods and the traditional forms. Three important branches of statistical reasoning are frequentists, Bayesians, likelihoodists. Bayesians and frequentists actually differ on the definition of probability. To a frequentist, probability is just the long‐run proportion of times that some event occurs in a controlled setting that assures iid sampling, which comes from their fundamental idea of replicability of the data generation process. All Bayesian hypothesis testing produces probability statements about the parameters of interest or the hypotheses. The chapter describes change‐point analysis of thermonuclear testing data.